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The research article is the analysis of wave propagation in an initially stressed micropolar fractional-order derivative thermoelastic diffusion medium with voids. The governing equations in the context of generalized fractional-order derivative thermo-elasticity are formulated and the velocity equations are obtained. The plane wave solution of these equations indicates the existence of six plane waves, namely coupled longitudinal displacement ( c L ), coupled thermal ( c T ), coupled mass diffusion ( c M D ), coupled longitudinal void volume fraction ( c V ), coupled transverse displacement ( c T D ), and coupled transverse micro-rotational ( c T M ) waves. The sets of coupled waves ( c L ), ( c T ), ( c M D ) and ( c V ) are found to be dispersive, attenuating and influenced by the presence of thermal, diffusion and voids parameters in the medium. The speeds of coupled transverse displacement ( c T D ), and coupled transverse micro-rotational ( c T M ) waves are not affected by thermal, diffusion and void parameters. The speeds of the plane waves, c L , c T , c M D , and c V are computed for a particular material and plotted against the thermal parameter, frequency, initial stress, diffusion and void parameters.

The semiconductor elastic medium in the context of the photothermal theory under the influence of rotation field is studied. A novel model of the governing equations is investigated due to the refined multi-phase-lags with the thermal relaxation times of the heat equation with the hydrostatic initial stress during transport process of the photothermal phenomenon. The interaction between the multi-waves of elastic-thermal-plasma is obtained. The normal mode method in the two dimensions is applied to obtain the exact solutions of the basic physical quantities under investigation. Plasma, thermal and mechanical loads have been applied on the free surface of the semi-infinite semiconductor elastic medium to get the complete solutions of the basic physical fields. Some comparisons are shown graphically and they are discussed as a function of thermal memories with the variation of some parameters. Silicon (Si) material is used to make the numerical simulation and to display the sensitivity to the variation of the rotation parameter.

Building on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

Investigated is a novel model in the photo-thermoelasticity theory that takes into account the impact of porosity and initial stress. A generalized photo-thermoelastic that is initially stressed and has voids is taken into consideration for the general plane strain problem. The solutions for the fundamental variables in two dimensions are obtained using the Laplace–Fourier transforms method in two dimensions (2D). Physical fields such as temperature, carrier concentration, normal displacement, and change in volume fraction field can all be solved analytically. The plasma of electrons, thermal load, and mechanical boundary conditions at the porosity medium’s free surface are used to show certain illustrations. The context of the Laplace–Fourier transformation inversion operations yields complete solutions. To complete the numerical simulation and compare several thermal memories under the influence of the porosity parameters, silicon (Si), a semiconductor porosity material, is used. The main physical variables are described and graphically displayed with the new parameters.

In this article, the effect of the magnetic field, initial stress, rotation, and nonhomogeneity on the radial displacement and the corresponding stresses in orthotropic material is investigated. The analytical solution for the elastodynamic equation is solved in terms of displacements. The variation of stresses, displacement, and perturbation magnetic field have been shown graphically. Comparisons are made with the previous results in the absence of the magnetic field, the initial stress, the rotation, and nonhomogeneity., В статье исследовано влияние магнитного поля, начального напряжения, вращения и неоднородности на радиальное смещение и соответствующие напряжения в ортотропном материале. Получено аналитическое решение уравнения эластодинамики в терминах смещения. Изменение напряжений, смещения и возмущений магнитного поля представлено графически. Проведено сравнение результатов с предыдущими данными, полученными при отсутствии магнитного поля, начального напряжения, вращения и неоднородности.

To study the acoustic emission evolution characteristics of saturated limestone under different loading and unloading paths, three cyclic loading and unloading tests were conducted with different loading rates and initial cyclic peak stresses, and acoustic emission monitoring was performed simultaneously. The results indicate that, during loading and unloading, the intermediate-frequency signals of saturated rock exhibit a variation trend of sparse–dense–sparse signals, whereas the low-frequency signals are continuously and massively produced. With the increase in the loading rate, the development trends of cumulative hits and energy become closer, and the development form of ringing count changes from N-type to U-type and then to N-type. The slight increase period and attenuation period are extended, whereas the intense growth period and postpeak calm period are shortened. With an increase in the initial cyclic peak stress, the change in cumulative energy is more obvious than that in cumulative hits near the rock failure. The development form of the ringing count changes from U-type to W-type and then to N-type, and each period is first shortened and then extended. With the increase in loading rate, the increase in the slow-change period tends to change from gradually increasing to increasing and then decreasing. By contrast, the increase in the step tends to change to a gradual increase. With the increase in the initial cyclic peak stress, the duration of and increase in the energy in the step and the slow-change period tend to decrease and then increase.

A novel theoretical mathematical-physics model is obtained when the microstretch properties of elastic semiconductor medium are taken into account. This model is investigated in the context of photo-excitation transport processes through the thermoelasticity theory. The new model can be called Microstretch-photo-thermoelasticity (MPT) theory. The MPT model is studied under the impact of hydrostatic initial stress. The carrier’s charge field (carrier density or plasma wave) appears due to optical excitation. In this model, the interaction between thermal-mechanical-plasma waves is obtained when the medium is in a rotating case. When the medium is linear, isotropic and homogenous, the two-dimensional (2D) elastic and electronic deformations governing equations are investigated. This is done while taking into account the microinertia of the medium particles. The basic physical variables are obtained using the mathematical plane harmonic wave technique to obtain the general solutions. The complete analytical solutions are solved when conditions from mechanical-thermal and plasma type act at the free surface of the medium. The silicon (Si) and Germanium (Ge) materials are used to make the numerical simulations. The numerical results are displayed graphically and discussed.

The present research deals with the mathematical model for study of the disturbance due to mechanical (horizontal or vertical) and thermal source in two dimensional transversely isotropic magneto thermoelastic solid under initial stress due to time-harmonic source with generalized Lord–Shulman (LS) theory of thermoelasticity with two temperatures. The Fourier transform has been used to find the solution of the problem. The displacement components, stress components and temperature distribution are calculated numerically in the transformed domain. The effect of time harmonic source, relaxation time and initial stress is depicted graphically on the resulting quantities for the insulated boundary and the temperature gradient boundary.

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Although most casting and heat treatment processes generate significantly high residual stress in the products, this factor is generally not taken into account in the design stage of the product. In this study, experimental study and numerical analysis were conducted on a constant stress beam to examine effects of the residual stress generated during the heat treatment process on yielding behavior of the product in use. A constant stress beam of SUS 304 was designed in order to test the stress behavior related to residual stress. The residual stresses generated during quenching heat treatment of the beam were measured in advance by ESPI (Electronic Speckle-Pattern Interferometry) equipment, and then the external stresses generated while applying a simple external load on the beam were measured. Also, the residual stress distribution generated during the heat treatment process was computed using a numerical analysis program designed for analyzing heat treatment processes. Then, the stress distribution by a simple external load to the beam was combined with the calculated residual stress results of the previous heat treatment step. Finally, the results were compared with experimental ones. Simulation results were in good agreement with the experimental results. Consistency between experimental results and computational results prove that residual stress has significant effects on the stress behavior of mechanical parts. Therefore, the residual stress generated in the previous heat treatment step of casting must be taken into account in the stage of mechanical product design. Highlights The bigger compressive residual stress occurs, the closer surface. When the residual stress is close to plastic deformation, the stress by external load did not significantly change. The residual stress generated during the manufacturing process should be considered in the design stage.

The paper aims to study, the effect of rigid boundary on the propagation of torsional surface waves in initially stressed gravitating dry sandy half space. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate. The expansion of the Whittaker function up to quadratic terms shows two such wave fronts may exist in the medium. Finally, it is concluded that the sandy medium without support of a gravity field cannot allow the propagation of torsional surface waves, where as the presence of gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy. Numerical results analyzing the velocity equations are discussed and presented graphically. It has been observed that density, rigidities play an important role for the propagation of torsional surface waves. It has been seen that as the non-homogeneity parameter in the layer increases, the velocity of torsional surface wave also increases. It has also been observed that an increase in compressive initial stresses decreases the velocity of torsional surface wave.

This paper aims to study the propagation of surface wave in two initially stressed heterogeneous magnetoelastic transversely isotropic media lying over a transversely isotropic half-space under the action of gravity. Heterogeneities of both the layers are caused due to exponential variation in elastic parameters. Dispersion relation is obtained in closed form by using Whittaker's asymptotic expansion. Magnetoelastic coupling parameters, heterogeneity, horizontal compressive initial stress and gravity parameters have remarkable effect on the phase velocity of surface wave. The obtained dispersion relation is found to be in well agreement with the classical Love-wave equation. Comparative study and graphical illustration has been made to exhibit the outcomes.

The intermediate results of the study of planar problems about perturbation by movable surface load of multilayer base with initial (residual) stresses are presented. Within the bounds of linearizired theory of elasticity for bodies with initial stresses there are considered the statement and method of solving a planar problem of the perturbation of the surface load moving with a constant speed of two-layered pre-stressed stripe with the rigid basis. The model of the layered medium “a plate and pre-stressed layer” is considered. Equations of plate motion are written taking into account the shift and rotary inertia. Layer material is assumed compressible, isotropic in the natural state. The form of elastic potential has a general form and must be specified only while implementation of numeral calculations. With the help of the Fourier integral transform method a fundamental solution to the problem is obtained in general form under various conditions of contact and speeds of load.

In the modelling process of cardiovascular diseases, one often comes across the numerical simulation of the blood vessel wall. When the vessel geometry is patient-specific and is obtained in vivo via medical imaging, the stress distribution throughout the vessel wall is unknown. However, simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall. In this work a computational method is formulated to restore the zero-pressure geometry of patient-specific blood vessels, and to recover the in vivo stress field of the loaded structures at the moment of imaging. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations. As only an update of the mesh is required, the formulation of this method allows for a straightforward implementation in combination with existing structural solvers, even if the structural solver is a black box.

Initial stress (pre-stress) in functionally graded material (FGM) structures is often inevitable because of the limitation of available manufacturing technology. On the basis of the “mechanics of incremental deformations”, the circumferential wave characteristics in FGM cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. Through numerical examples, the convergence of the polynomial method is discussed. The influences of the initial stresses on the circumferential Lamb-like and the circumferential SH waves are investigated, respectively. Numerical results show that they are quite distinct. Moreover, the influences of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.

In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.

We consider a initially stressed hyperelastic body in equilibrium in its undeformed configuration under a system of dead loads. We give sufficient conditions on the stored energy which guarantee that when the loads undergo a small perturbation, the energy functional Γ converges, after some re-scaling, to the energy functional of linear elasticity with initial stress. We also show, under stronger conditions, that quasi-minimizers of the non-linear problem converge to a minimizer of the incremental problem.

The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

This paper investigates the dynamic response to a moving load of a system comprising an initially stressed covering layer and initially stressed half-plane, within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It was assumed that the materials of the layer and half-plane are anisotropic (orthotropic), and that the velocity of the line-located moving load is constant as it acts on the free face of the covering layer. The investigations were made for a two-dimensional problem (plane-strain state) under subsonic velocity of the moving load for complete and incomplete contact conditions. Corresponding numerical results were obtained for the stiffer layer and soft half-plane system in which the modulus of elasticity of the covering layer material (for the moving direction of the load) is greater than that of the half-plane material, which was assumed to be isotropic. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it was established that, the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the initial stretching of the covering layer causes to increase these values.

In this paper, Love waves in a heterogeneous orthotropic layer under changeable initial stress over a gravitating porous halfspace

An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or growth and remodelling in living materials. For this reason it is useful to develop a mechanical framework of initially stressed solids irrespective of how this stress formed. An ideal way to do this is to write the free energy density $\Psi= \Psi(\boldsymbol F, \boldsymbol {\tau})$ in terms of initial stress $\boldsymbol \tau$ and the elastic deformation gradient $\boldsymbol F$. In this paper we present a new constitutive condition for initially stressed materials, which we call the initial stress symmetry (ISS). We focus on two consequences of this symmetry. First we examine how ISS restricts the free energy density $\Psi = \Psi (\boldsymbol F, \boldsymbol \tau) $ and present two examples of $\Psi (\boldsymbol F, \boldsymbol \tau)$ that satisfy ISS. Second we show that the initial stress can be derived from the Cauchy stress and the elastic deformation gradient. To illustrate we take an example from biomechanics and calculate the optimal Cauchy stress within an artery subjected to internal pressure. We then use ISS to derive the optimal target residual stress for the material to achieve after remodelling., Comment: 25 pages, 10 figures

In this work the effect of initial twist on wave characteristics in a prestressed elastic thin tube filled with a viscous fluid is studied. Initially the tube is subjected to a large static transmural pressure P i , an axial stretch λ z , and a twisting moment M. Assuming that in the course of fluid flow a small incremental axially symmetric disturbance is added on this field the equations governing the incremental motion are obtained both for elastic tube and viscous fluid. Seeking a harmonic wave type of solution to the field equations and using the boundary conditions the dispersion relation is obtained for long-wave approximation. Considering the difficulties of analytical treatment of the dispersion equation a numerical analysis is presented and the results are discussed.

On the basis of the general nonlinear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stress-dependent tensor of incremental elastic moduli. In considering three special cases of initial stress within the general framework, namely hydrostatic stress, uniaxial stress and planar shear stress, we then elucidate in general form the dependence of various elastic moduli on the initial stress. In each case the effect of initial stress on the wave speed of homogeneous plane waves is studied and it is shown how various special theories from the earlier literature fit within the general framework. We then consider the situation in which the initial stress is a pre-stress associated with a finite deformation and, in particular, we discuss the specialization to the second-order theory of elasticity and highlight connections between several classical approaches to the topic, again with special reference to the influence of higher-order terms on the speed of homogeneous plane waves. Some discrepancies arising in the earlier literature are noted., Comment: 39 pages

The purpose of the present article is the study of the effect of the gravity field on an initially stressed micropolar thermoelastic medium with microtemperatures. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. The comparisons are established graphically in the presence and the absence of gravity, initial stress and micropolar thermoelasticity. The main conclusions state that the gravity, initial stress and the micropolar thermoelasticity are effective physical operators on the variation of the physical quantities. The microtemperatures are very useful theory in the field of geophysics and earthquake engineering.

In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by coupling stiffness matrices. Since the global and local meshes can be generated independently, mesh generation efforts are reduced remarkably. However, s-FEM has a common issue. The generation of coupling stiffness matrices takes a considerable amount of program development efforts, which include constructing accurate cross-element integration methodology and programming it for various element types. For such an issue, we propose an iterative s-FEM that does not require the generation of coupling stiffness matrices at all. The coupling term is now evaluated by global and local stresses that are computed on the respective mesh and then transferred to the other by interpolation techniques. The global and local stresses are treated as initial stress in the finite element computations. The global and local analyses are performed alternately under assumed initial stress, and converged solution is achieved by iteration with a monitored residual being sufficiently small. In proposed iterative s-FEM, an issue about linear independence of global and local elements, which is known to occur in the original s-FEM, does not occur. In numerical experiments, converged solution was successfully obtained within several hundred iteration counts. Accurate stress distribution for a stress concentration problem and an accurate stress intensity factor for a linear elastic fracture mechanics problem were computed by proposed iterative s-FEM. In addition, several stress interpolation techniques were compared in the numerical experiments. Nearest neighbor interpolation for the global stress and local least squares interpolation for the local stress showed good convergence and accurate solution.

Rayleigh wave propagation in an isotropic homogeneous initially stressed thermoelastic half-space under the effect of magnetic field has been studied using Green–Lindsay (GL) theory of generalized thermoelasticity. The frequency equation has been obtained for Rayleigh waves. The Rayleigh wave velocity is computed numerically for different values of initial stress parameter, magnetic pressure number, thermoelastic coupling parameter, and wave number for aluminium material, and the results obtained are compared graphically.

Modelling of SH-waves in an anisotropic fiber-reinforced layer provides a great deal of sup-port in the understanding of seismic wave propagation. This paper deals with the propa-gation of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space. The heterogeneity of the elastic half-space is caused by linear variations of density and rigidity. As a special case when both media are homogeneous and stress free, the derived equation is in agreement with the general equation of the Love wave. Numerically, it is ob-served that the velocity of SH-waves decreases with an increase in heterogeneity-reinforced parameters and decrease in initial stress.